[95.05] Gamma-Ray Bursts Show that the Star Formation Rate Rises Steeply Between Red Shifts From 2 To 6

Two different luminosity indicators have recently been
proposed for Gamma Ray Bursts that use gamma ray
observations alone. They relate the burst luminosity, L,
with the time lag between peaks in hard and soft energies,
Tlag, and the spikiness or variability of the burst's
light curve, V. These relations are currently justified
and calibrated with only 6 or 7 bursts with known red
shifts. We have examined BATSE data for Tlag and V
for many bursts. (1) A strong correlation between Tlag
and V exists, and it is exactly as predicted from the two
proposed relations. This is proof that both luminosity
indicators are reliable. (2) We have combined the
luminosities as derived from both indicators as a means to
improve the statistical and systematic accuracy when
compared to the accuracy from either method alone. The
result is that we have 112 bursts with good luminosities and
hence red shifts. (3) The burst luminosity function is a
broken power law, with the break at L=1052erg. The
numbers in logarithmic bins scale as L-2.0+-0.2 above
the break and as L0.4+-0.4 below the break. (4) The
number density of GRBs varies with red shift roughly as
(1+z)2.3+-1.0 from z=0.4 to z~6. The burst number
density is proportional to the star formation rate since
bursts are seen to be associated with star forming regions
and since they are produced with little delay by massive
stars. So we conclude that the star formation rate in our
Universe is rising steeply for red shifts between 2 and ~6,
in contrast to optical results which show a flat rate at
most. This new method (using gamma radiation) does not
suffer any problems from extinction, and this is a
substantial advantage over the older methods (using optical
light) which can suffer greatly from extinction.